Geostatistical Model Resolution Enhancement in the Context of Multiple-Point Statistics

TL;DR

This paper proposes a method to generate higher-resolution geostatistical models using multiple-point statistics by directly rescaling the training image, addressing scale-dependence issues in spatial structure modeling.

Contribution

It introduces a novel approach of directly rescaling the training image to enhance model resolution in multiple-point statistics, overcoming challenges in scale-dependent variability characterization.

Findings

Direct rescaling of training images effectively increases model resolution.

Scale-dependence of spatial structure poses challenges in high-order statistics.

Rescaling approach simplifies the generation of high-resolution models.

Abstract

Current multiple-point based simulations implementations generate geostatistical models at the scale of the training image; there is an assumption that the categories are exclusive at smaller scales. The goal of this paper is to generate models with multiple-point statistics (MPS) at a higher resolution than that of the available training image. This paper addresses model resolution enhancement by studying the scale-dependence of spatial structure in MPS based models -- extrapolating the smaller scale MPS from the larger scale MPS, and (2) rescaling the training image directly to the smaller scale. The first approach investigates the MPS probabilities. A number of challenges in characterizing smaller scale variability using high-order statistics are documented. The paper concludes by advocating the direct rescaling of the training image to generate models at higher resolution.